How to maximize farm production?

Build and upgrade all of the farms that are available to you and make sure you complete the research in city development to boost the production. Plus be in a good alliance with technology donations that is able to research the food related alliance tech.

Recruit and station the heroes that boost the farm production. Pioneer, Lt. Joshua, Green Thumb, all help. Level them up and unlock their skills.

Be a Farmer class. This will give you buffs on production rates and let you gain extra resources with the farmer building.